The purpose of this paper is to demonstrate that, for globally minimize one dimensional nonconvex problems withboth twice differentiable function and constraint, we can propose an efficientalgorithm based on Branch and Bound techniques. The method is firstdisplayed in the simple case with an interval constraint. The extension is displayedafterwards to the general case with an additional nonconvex twicedifferentiable constraint. A quadratic bounding function which is betterthan the well known linear underestimator is proposed while w-subdivision is added to support the branching procedure. Computational results on several andvarious types of functions show the efficiency of our algorithms and theirsuperiority with respect to the existing methods.
